hpsc.gov.in : HCS Preliminary Examination Mathematics Question Paper

Name of the Organization : Haryana Public Service Commission
Name of the Exam : HCS Preliminary Examination
Subject : Mathematics
Document Type : Previous Question Paper
Year : 2014

Website : http://hpsc.gov.in/en-us/
Download Sample/Model Question Paper : https://www.pdfquestion.in/uploads/11246-Math.pdf

HPSC Mathematics Question Paper

Code :- 12
Time Allowed : Two Hours
Marks: 100

 Related : HPSC HCS Preliminary Exam Law Question Paper : www.pdfquestion.in/11241.html

Instruction

Read instructions given below before opening this booklet :
** Use only BLUE Ball Point Pen.
** In case of any defect – Misprint, Missing Question/s Get the booklet changed.

** No complaint shall be entertained after the examination.
** Before you mark the answer, read the instruction on the OMR Sheet (Answer Sheet) also before attempting the questions and fill the particulars in the ANSWER SHEET carefully and correctly.

** There will be no Negative Marking.
** Answer Sheets will be collected after the completion of examination and no candidate shall be allowed to leave the examination hall earlier.
** The candidates are to ensure that the Answer Sheet is handed over to the room invigilator only.

** Rough work, if any, can be done on space provided at the end of the Question Booklet itself. No extra sheet will be provided in any circumstances.
** Write the BOOKLET SERIES in the space provided in the answer sheet, by darkening the corresponding circles.
** Regarding incorrect questions or answers etc. Candidates kindly see NOTE at the last page of the Booklet.

Model Questions

Q.l If A is a (3×3) non-singular matrix such that AAT = AT A and B = A-1AT,then BBT is
(A)1+B
(B)I
(c) A+B
(D) AB

Q.2 If A is a (2×2) non-singular matrix, then the value of adj (adj) A) is
(A) A
(B) I
(c) A2
(D) -A

Q.3 Let P and Q be (3×3) matrices with P*Q. If p3=q3nd P2q-q2P, then the determinant of (P2+Q2) is
(A) 1
(B) 0
(c) 2
(D)-2

Q.4 If A & B are (nxn) matrices, then which of the following statements is generally invalid
(A) If A4 has an inverse, so has A
(B) If AB has an inverse, so has B
(C)la,a| = alAl, for any positive value of a
(D)|A| BA| = lAllBl

Q.5 If A is the singular matrix then A(adj A) is
(A) Identity matrix
(B) null matrix
(C) scalar matrix
(D) symmetric matrix

Q.6 If A is skew symmetric matrix of order (n x n), then the trace of A is
(A) n
(B) -n
(c) 0
(D) n2

Q.7 If A is a non-singular matrix of order 3 such that |adj A| = 225, then |A| is
(A) 225
(B) 25
(c) l5
(D) 20

Q.8 The largest value of a third order determinant, whose elements are 0 or 1 is
(A) 1
(B) 0
(c) 2
(D) 3

Q.9 If P(1,2),Q(4,6), R(5,7) and S(a,b) are the vertices of a parallelogram PQRS, then (a , b) is
(A) (2,4)
(B) (3,4)
(c) (2,3)
(D) (3,5)

Q.10 The distance between the parallel lines y = 2x+4 and 6x = 3y + 5 is
(A) 17/3
(B) 1
(C) 3
(D) 17/5

11. An equation of a plane parallel to the plane x -Zy *22 = 5 and at a unit distance from origin is
(A)r-2y*22=3
(B)r-2Y*22=-t
(C)x – 2y *22 = 7
(D)x – 2Y *22 = -S

12. The length of the diameter of the circle which touches the x axis at the point (1,0) and passes through the point (2,3) is
A) l0/3
(B) 3/s
(C) 6/5
(D) 5/3

13. If two tangents are drawn from a point P to the parabola y2:4xare at right angles, then the locus of Pis
(A) 2x+1:0
(B) x:-l
(C) 2x-l-0
(D) x-l

14. If the vectors a= i – j +2k,8 = 2i* 4j + k,c = 7i+ i + 1tk are mutually orthogonal, then (.1,p) is
(A) (2,-3)
(B) (-2,3)
(C) (3,-2)
(D) (-3,2)

15. 22:The circles 2*y’=4x*8y*5, intersect the line 3x-4y= m at two distinct point
(A)-35 < m175
(B) 15 <m<65
(C)35 <m < 85
(D)-85<m< -35

16 If at = b! = cz and a,b,c are in G.P., thenx,y,z arein
(A) AP
(B) GP
(C) HP
(D) x=Y=z

17. The HM of two numbers is 4. If the arithmetic mean A and geometric mean G satisff the relation 2A+G2=27, then the numbers are
(A) 6,3
(B) s,4
(C) s,-512
(D) -3,1

18. If 2a+3b+6c=0, then at least one root of the equation axz + bx * c = 0, lies in the interval
(A) (0, l)
(B) (1,2)
(c) (2,3)
(D) (3,4)

19. An asymptote to the curve x3 + y3 – 3xy = Ois x+ y+a : 0′ then the value of a is
(A) -l
(B) I
(C) A
(D)

20. The curve in which the slope of the tangent at any point equal to the ratio of abscissa to the ordinate of the point is an
(A) Ellipse
(B) Parabola
(C) Rectangular hyperbola
(D) Circle